In sub-sampling and sample rate decimating discrete time systems it is necessary to suppress interferers whose frequencies fall within the aliasing bandwidths of the particular system. For this reason, anti-aliasing filters are used to suppress these interferers. The requirements of these anti-aliasing filters, however, are typically very demanding due to the level of interference encountered, bandwidths of the desired and interfering signals, desired suppression, etc. The demanding requirements of the anti-aliasing filter typically results in having to design in costly analog filters or high gate count digital filters. In some cases, it is too cost prohibitive to include an anti-aliasing filter in the system and performance is therefore compromised, for example, in very low cost consumer applications.
A block diagram illustrating an example prior art decimation circuit where an interfering signal is combined with a desired signal to generate an alias bandwidth at the output is shown in FIG. 1. The circuit, generally referenced 100, is a test circuit constructed to demonstrate the problems associated with the prior art. The circuit 100 comprises a desired signal generator input 102, interfering signal generator 104, amplifier 106, summer 108, optional low pass filter (LPF) 110, decimation by 32 112, integrator 114 and display 116.
In this example test circuit, the desired signal having a frequency of 0.4 Hz and an interfering signal at 74.4 Hz are both sampled at 2.4 kHz and summed together at summer 108. A diagram illustrating the frequency spectrum of the input to the prior art decimation circuit of FIG. 1 including the desired and interfering signals is shown in FIG. 2. The frequency spectrum shown represents the signal at the output of the summer 108. The desired signal 200 is centered around 0.4 Hz and the interferer signal 202 is at 74.4 Hz. Note that if 30 dB suppression is desired a 30 dB low pass filter (110 in FIG. 1) is required to sufficiently suppress the interferer signal.
Consider the circuit 100 without optional filter 110. Since there is no filter, the input signal must be sampled at twice the maximum frequency, i.e. the Nyquist rate. As the sampling rate is decreased, the more signals fold into the bandwidth of interest and interfere with the desired signal. Therefore, an anti-aliasing filter is required before the decimation block 112.
The summed signal is then injected into the downsample by 32 block 112 thus yielding an effective sampling rate of 75 Hz, i.e. 2400 Hz/32. The output of the decimation block is analyzed and presented on the display. A diagram illustrating the frequency spectrum of the output from the prior art decimation circuit of FIG. 1 including the desired and interfering signals is shown in FIG. 3. The peak 300 represents the original desired 0.4 Hz signal and the peak 302 represents the aliased 74.4 Hz signal. Due to the decimation and resulting effective sampling rate of 75 Hz, the interfering signal has folded very close to the desired signal lying only 0.2 Hz away. It is important to note that if the interferer signal had a frequency of 74.6 Hz, it would have folded directly on top of the desired signal. Clearly, this situation is not desirable and in most systems, an anti-aliasing filter would have to be introduced before the decimation. A disadvantage, however, is that good (i.e. high suppression) filters are costly in terms of complexity, size and current consumption.
Bluetooth is a worldwide specification for a small low-cost radio. Bluetooth networks are intended to link mobile computers, mobile phones, other portable handheld devices and provide Internet connectivity. Bluetooth uses a packet switching protocol employing frequency hopping at 1600 hops/s with a maximum data rate of 1 Mb/s. Bluetooth radios operate in the unlicensed ISM band at 2.4 GHz. A frequency hop transceiver is used to combat interference and fading and a shaped, binary FM modulation is applied to minimize transceiver complexity. The symbol rate is 1 Ms/s. For full duplex transmission, a Time-Division Duplex (TDD) scheme is used. On the channel, information is exchanged through packets. Each packet is transmitted on a different hop frequency. A packet nominally covers a single slot, but can be extended to cover up to five slots.
The slotted channel is divided into time slots, each having a nominal slot length of 625 μs. The time slots are numbered according to the Bluetooth clock of the piconet master. The slot numbering ranges from 0 to 227−1 and is cyclic with a cycle length of 227. In the time slots, master and slave can transmit packets. A time-division duplex (TDD) scheme is used where master and slave alternatively transmit. The master starts its transmission in even-numbered time slots only, and the slave starts its transmission in odd-numbered time slots only. The packet start is aligned with the slot start.
Consider a Bluetooth receiver implemented as a sub-sampling system. According to the Nyquist theorem proper sampling requires the input be sampled at least at twice the highest frequency, i.e. the Nyquist sampling rate, otherwise aliasing problems will be introduced. Often times and in the case of Bluetooth, sampling at twice the highest frequency is very difficult to do since the input has a very wide bandwidth requiring sampling at very high speeds. To get around this, the input is instead sampled at lower speeds and a filter is placed at the front to reduce the bandwidth of interest. The filter removes potentially interfering signals that would otherwise be problematic after sampling. The problem, however, is that often very narrow band filters are required which are very expensive in terms of complexity, size and cost.
There is thus a need for a mechanism to either eliminate or reduce the requirements of the anti-aliasing filter that is required to remove interfering signals from the output signal in decimating and sub-sampling discrete time systems.